CAT geometry questions are based on topics such as Similar and Congruent Triangles, Quadrant Systems and others. This section comes under the CAT Quantitative Aptitude section. The students can keep the formulae handy to revise during the last minute of the exam.
CAT geometry questions are asked in the Quantitative Aptitude Section of the CAT exam. CAT geometry problems such as Line Equations, Circle equations, Special triangles, Total Surface, Area, Similar and Congruent Triangles, and Theorems are asked in the exam.
Approximately 10-12% percent of the section contains topics from Geometry.
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CAT Geometry Questions
Various challenging CAT geometry questions, as well as easy ones, are asked in the Quantitative Aptitude section. Below are some sample questions of CAT Geometry Questions candidates can refer to. For the answer keys of the provided questions below and more such practice questions, candidates can find the CAT Geometry Questions sample PDF at the end in a table below.
Ques. 1) ABCD is a rhombus with the diagonals AC and BD intersecting at the origin on the x-y plane. The equation of the straight line AD is x + y = 1. What is the equation of BC?
Options:
1. x + y = –1
2. x – y = –1
3. x + y = 1
4. None of the above
Ques. 2) If a, b and c are the sides of a triangle, and a2+ b2+ c2= bc + ca + ab, then the triangle is:
Options:
1. Equilateral
2. Isosceles
3. right-angled
4. obtuse-angled
Ques. 3) A certain city has a circular wall around it, and this wall has four gates pointing north, south, east and west. A house stands outside the city, 3 km north of the north gate, and it can just be seen from a point 9 km east of the south gate.
What is the diameter of the wall that surrounds the city?
Options:
1. 6 km
2. 9 km
3. 12 km
4. None of the above
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Ques. 4) A ladder leans against a vertical wall. The top of the ladder is 8 m above the ground. When the bottom of the ladder is moved 2 m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?
Options:
1. 10 m
2. 15 m
3. 20 m
4. 17 m
Ques. 5) Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10.Its area is 80. What is the exact length of its third side?
Options:
1.260
2.250
3.270
4.270
Ques. 6) A rectangular pool 20 m wide and 60 m long is surrounded by a walkway of uniform width. If the total area of the walkway is 516m2,how wide, in metres, is the walkway?
Options:
1. 43 m
2. 4.3m
3. 3 m
4. 3.5 m
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Ques. 7) The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, is:
Options:
1. 24 cm
2. 25 cm
3. 15 cm
4. 20 cm
Ques. 8) Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the centre. Find the ungrazed area.
Options:
1. 22 m2
2. 42 m2
3. 84 m2
4. 168 m2
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CAT Geometry Topics
Various topics are covered in the Geometry section. Candidates may refer to the complete list of Geometry topics asked in the CAT exam.
- Cyclic Quadrilateral
- Areas and Formulas of: Hexagonal Polygon, Triangle, and Rectangle. Square, Rhombus, Trapezoid
- Quadrant System
- Distance between Two Lines
- Angles: Supplementary, Complementary, Obtuse, Acute, and Right
- Line Equation and Circle Equation
- Special Triangle
- Total Surface Area
- Lateral Surface Area of Different Solids such as Cubes, Cuboids, Cylinders, Pyramids, Cones, Spheres, Hemispheres, and Frustum
- Circumradius and Inradius
- Similar and Congruent Triangle
- Theorems: Pythagoras, Midpoint, Apollonius, Basic Proportionality, Internal and External Angular Bisector, and others.
- Volume
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Coordinate Geometry Formulae
It is important to know that in the CAT Quantitative Aptitude section, along with Geometry questions, topics on Mensuration are also asked. Below are some basic formulas of CAT Coordinate Geometry and Mensuration.
| CAT Coordinate Geometry and Mensuration Formulas | |
| The Equation of a Line Using One Point and the Gradient | y – y1 = m(x – x1) |
| The Distance Between two Points A(x1, y1) and B(x2, y2): | AB² = (x2 – x1)² + (y2 – y1)² |
| The Midpoint of a Line Joining Two Points | [(x1 + x2)/1, (y1 + y2)/2] |
| Rectangle | Area = lb |
| Perimeter = 2(l+b) | |
| Circle |
Area = πr² or πd²/4 |
| Circumference = 2πr or πd | |
| Area of sector of a circle = (θπr² )/360 | |
| Square | Area = a × a |
| Perimeter = 4a | |
| Triangle | √[s(s – a)(s – b)(s – c)], where s = (a + b + c)/2 |
| Cube | Volume: V = a3 |
| Lateral surface area = 4a² | |
| Surface Area: S = 6a2 | |
| Diagonal (d) = √3 a | |
| Cuboid | Volume of cuboid: lbhTotal surface area = 2 (lb + bh + hl) or 6l2Length of diagonal =√(l² + b² + h²) |
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